Monochromatic light of wavelength 632.8nm is generated by a helium-neon laser having a power of 9.42mW. Evaluate the following:

Energy and momentum of each photon
The number of photons emitted per second
The speed of a hydrogen atom to have momentum equal to that of an emitted photon by the laser.

Answer:

Given, λ = 632×10-9nm, P = 9.42×10-3W

1. Energy of a photon is given by: E = hv = hc/λ

E = 6.6 x 10-34 3 x 108 / 632.8 x 10-9 = 3.12 x 10-19 J = 3.13 eV

Momentum of the photon is given by: p = hv/c = h/λ

P = 6.6 x 10-34 3 x 108 / 632.8 x 10-9 = 1.043 x 10-27 kg/ms

b. Number of photons emitted per second (n) will be given by the equation:

Power = n × energy of a photon

9.42×10-3 W = n × 3.13×10-19 J

To find the speed of a hydrogen atom (v) to have momentum same as a photon:

v = p/m

Here, p = momentum of photon = 1.043×10-27 kgm/s, and

M = mass of a hydrogen atom which is equal to 1.67×10-24kg

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